To find the equation of the normal to a curve at a point

You need to follow 4 steps:
  1. First differentiate the equation of the curve to get the slope of the tangent at each point.
  2. Evaluate the differential at the point required to get the slope of the tangent at that point.
  3. Now calculate the slope of the normal at that point. If the slope of the tangent is t, then the slope of the normal is -1/t.
  4. Finally, the equation of the line is y=-x/t + c, substitute the values of x and y to find c.

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